The need for linkage and segregation analysis programs for general pedigrees that can handle epistatic effects of several genes, and multiple marker loci, is generally recognized. The approach to this goal taken in this project has three distinctive aspects: 1) Inclusion of pleiotropic effects on several qualitative or quantitative traits. 2) A Bayesian perspective on linkage and segregation analysis that is, so to speak, half-way between model-dependent and non-parametric methods. 3) A conservative approach to Markov chain Monte Carlo, using it primarily in contexts where it is possible to find lower bounds on its rate of convergence.